The medial entorhinal cortex (MEC) is part of a neural system for mapping a subject's position within a physical environment. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations, and are organized in modules which collectively form a population code for the animal's allocentric position1. The invariance of the correlation structure of this population code across environments and behavioural states, independently of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained elusive due to the small samples of cells obtained to date. Here we show, with simultaneous recordings from many hundreds of grid cells, and subsequent topological data analysis, that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to the moving animal's position in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained, with minimal distortion, between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feed-forward models where grid patterns are created from external inputs by Hebbian plasticity. This demonstration of network dynamics on a toroidal manifold provides the first population-level visualization of CAN dynamics in grid cells.
We have studied two newborn infants with a remarkable genital malformation, failure of urethral development with enormous bladder distension, atresia of the distal hindgut, vertebral abnormalities, and compression deformities. This is a pattern of anomalies similar to, and probably an extension of, the association of female pseudohermaphroditism and other anomalies (FPA) described by Lubinsky [Am J Med Genet 6:123-136, 19801. We propose that its pathogenesis involves a defect expressed in mesoderm, especially caudal mesoderm. We offer some speculation on what might be its nature, with particular reference to the theory of cell surface molecules having a role in morphogenesis. We apply the concept of the developmental field to provide a clarifying perspective.Key words: developmental field, axial mesodermal defect, caudal "regression," female pseudohermaphroditism, genital hypertrophy INTRODUCTIONA large number of disorders involve characteristic patterns of malformation of the caudal region, with various types and combinations of defects of urogenital tract, distal gut, caudal vertebral column, and lower limbs. To bring some order to the complexity of this clinical heterogeneity, commonalities may be sought at the phenotypic level [Kallkn and Winberg, 1974;Pinsky, 1978;Evans, 1982; Khoury et al, 19831, or in terms of an underlying process. A propos of the latter, a concept gaining currency is that of the developmental field [Opitz, 1979; Lubinsky, 1980 al, 1983; Optiz, 19851. After Lubinsky [1980], we may imagine a caudal developmental field, in which districts give rise to external genitalia, urogenital tract, distal gut, and other structures. What comprises the physical basis of this field may be an embryonic primordium destined to give rise to specific tissues, and through which may be bestowed vulnerability upon the processes of morphogenesis, leading to primary malformation. Further substance to this concept is afforded by reference to theories of the morphogenetic role of axial mesoderm [Russell et al, 1981; Jones et al, 19821; we may consider the identity of the embryonic primordium in question to be, in fact, mesoderm of axial origin and caudal destination.We apply these principles to a study of two infants with caudal malformations characterised in particular by excessive and distorted growth of the external genitalia. CLINICAL REPORTS Patient 1This baby boy was the 3rd child of nonconsanguineous parents of Anglo-Saxon origin, with two normal elder brothers. The father was 32 and the mother 31 years old at the birth of the infant. There is no known family history of a similar disorder or of diabetes. An attempted external version at 38 wk gestation was unsuccessful, presumably reflecting the oligohydramnios noted at birth. He was delivered at term from a breech position, weighing 3,610 gm. Major abnormalities were obvious (Fig. 1). The positioning of the limbs, especially the lower limbs, was distorted, with hip dislocation and external rotation on the left, and incurving on the right. The abdomen wa...
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